We had the opposite issue - the flooring in the room where we have relocated the kitchen is 1" lower than the flooring in the adjoining living room. We didn't realize this until we removed a wall between the new kitchen space and the new living room space. I did not raise the kitchen floor b/c it was too much money to do so (we also had other structural expenses that had priority over the floor). We have a transition piece between the two rooms (the opening is about 4'). It seems to be working well (we aren't back in the space yet). If you went back and changed the height of the floor after you do the kitchen, would you remove the cabinets to change the floor? I wouldn't think you would do that. Then your floor would be a different height under the cabinets than in the rest of the kitchen. I would do it all now or do a transition piece and keep the heights as they are.

#2 - insulated ceiling/air tight (IC/AT) is mandatory in many areas and always recommended if installing in a ceiling that is insulated, or should be. Most low voltage housings are only IC/AT if new construction type. Light shop was correct in recommending new construction. #3,4 - looking at attic for access does not mean that the housings will fit where desired unless they also carefully measured the layout to see what may be in the way of each fixture. The layout is generally done from below and projected up onto the ceiling with exploratory small holes to then locate in the attic. That the electrician found the space issues when starting the project should be foreseeable by him. How the electrician priced the project may reflect his experience. Low voltage new construction housings are generally larger and harder to place than non low voltage new construction housings. The fixture you ordered may be a brand or model he hasn't seen before. For example, Halo has a 3" low voltage fixture made for shallow depth but the housing is huge in length and width and can be quite a surprise if one hasn't used them before. If you don't need the shallow depth it is also a mistake to order that model. #5 - sounds like store does not stock the housings. Buying product that may or may not fit well from stores that don't stock and won't accept a return is risky. Electrician should try to put in the new construction. If you aren't in a mandatory IC/AT area then you can substitute remodel housings where necessary and at least limit the number you must return or eBay. And then there is the issue of why and how you ended up with the number and type of fixtures you are using but I'm sure others will add to the thread about that.

My first impression is that leveling the base cabinets on the carpet will be difficult as the carpet does not provide a firm surface. And many local building codes specify the electrical outlets in a situation like this have to be redone to be permanently affixed to the cabinet back---although that is really not a huge problem unless the outlet would need repair.

Holly - your response makes sense and is basically what we have here (although it is not FLUSH with the back - the back panel hangs over, which you can barely see in the picture above. But if this is true and how these are supposed to be, then why do the installation instructions say to drill pilot holes 1" from the side panels on each side. That wouldn't make it into the base at all. My husband installed it, the way gaucho advised above. It seems fine, although there is no oven in it yet. During install, we found cracks on both sides of the front (that go through from inside to outside) panels. (Attached a picture of the worst one.) I've sent pictures to the cabinet company we bought it from to see what is next. I think it should be replaced. Which mean DH has to take this one out and install again. Or they'll do nothing and we'll have cracked cabinet fronts to live with. Very annoying.